Chapter 7.3, Problem 99E

(a)

To determine

To graph: the function $f\left(x\right)=\sin 6x+\sin 7x$ .

Explanation of Solution

Given information:

Given function

  $f\left(x\right)=\sin 6x+\sin 7x$

Graph:

Now, consider the function.

  $f\left(x\right)=\sin 6x+\sin 7x$

Sketch the graph of the function using graphing utility.

  

(b)

To determine

To graph: the function $f\left(x\right)=2\cos \frac{x}{2}\sin \frac{13x}{2}$ .

Explanation of Solution

Given information:

Given function

  $f\left(x\right)=2\cos \frac{x}{2}\sin \frac{13x}{2}$

Graph:

Now, consider the function.

  $f\left(x\right)=2\cos \frac{x}{2}\sin \frac{13x}{2}$

Sketch the graph of the function using graphing utility.

  

(c)

To determine

To graph: the function $y=2\cos \frac{x}{2}$ and $y=-2\cos \frac{x}{2}$ in the same viewing window with $f\left(x\right)=\sin 6x+\sin 7x$ .

Explanation of Solution

Given information:

Given function

  $y=2\cos \frac{x}{2}$ and $y=-2\cos \frac{x}{2}$

Graph:

Now, consider the function.

  $y=2\cos \frac{x}{2}$ and $y=-2\cos \frac{x}{2}$

Sketch the graphs of the functions $f\left(x\right)=\sin 6x+\sin 7x$ , $y=2\cos \frac{x}{2}$ and $y=-2\cos \frac{x}{2}$

using graphing utility.

Interpretation:

Graphs of $y=2\cos \frac{x}{2}$ and $y=-2\cos \frac{x}{2}$ are treated as the boundary of $f\left(x\right)=\sin 6x+\sin 7x$ .